Education
Factorial Calculator
Last updated: May 31, 2026
Written by Blake Boege
A factorial calculator is a mathematical counting utility that computes the product of all positive integers less than or equal to n. It employs arbitrary-precision integer arithmetic to preserve exact digits for inputs above 20! and displays progress lists and scientific notation fallbacks.
Calculate the factorial (n!) of any whole non-negative integer up to 170 with step-by-step expansions. Employs BigInt accuracy to preserve full precision.
Quick Answer
Calculate factorials (n!) for non-negative integers up to 170. Get exact long integer values via BigInt, scientific notations, and full product expansions.
Accepts whole non-negative integers up to 170. · e.g. 5
What is a Factorial?
The factorial of a non-negative integer n is the product of all positive integers less than or equal to n.
n! = n × (n−1) × (n−2) × ... × 1
By convention, 0! = 1.
5!
120
Exact digits count: 3
Calculations are done with BigInt support, yielding exact values without losing precision at large inputs.
Factorial Step-by-Step Expansion
Examples
Small Integer: 5!
Result = 120 (5 × 4 × 3 × 2 × 1)
Medium Integer: 10!
Result = 3,628,800
Large Integer: 20!
Result = 2.4329 × 10^18 (Exact: 2,432,902,008,176,640,000)
How it works
The calculation multiply integers consecutively down to 1:
Recurrence Relation
n! = n · (n − 1)!
Where 0! is defined as 1.
Factorials reference list (0! to 20!)
| n | n! Value |
|---|---|
| 0! | 1 |
| 1! | 1 |
| 2! | 2 |
| 3! | 6 |
| 4! | 24 |
| 5! | 120 |
| 6! | 720 |
| 7! | 5,040 |
| 8! | 40,320 |
| 9! | 362,880 |
| 10! | 3,628,800 |
| 11! | 39,916,800 |
| 12! | 479,001,600 |
| 13! | 6,227,020,800 |
| 14! | 87,178,291,200 |
| 15! | 1,307,674,368,000 |
| 16! | 20,922,789,888,000 |
| 17! | 355,687,428,096,000 |
| 18! | 6,402,373,705,728,000 |
| 19! | 121,645,100,408,832,000 |
| 20! | 2,432,902,008,176,640,000 |
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Frequently asked questions
A factorial is the product of all positive integers less than or equal to a given non-negative integer 'n'. It is written as 'n!' (read as 'n factorial'). For example: 5! = 5 × 4 × 3 × 2 × 1 = 120.
In mathematics, defining 0! = 1 is logical and necessary for several reasons: (1) It represents the number of ways to arrange zero items (which is exactly 1 way: empty set). (2) It keeps the combinatorics formulas, like permutations P(n, r) and combinations C(n, r), consistent without causing division-by-zero errors. (3) It fits the algebraic recurrence relation (n-1)! = n! / n (where 0! = 1! / 1 = 1).
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800.
In standard computer systems using 64-bit floating-point numbers (Double precision), values overflow to Infinity at 171!. By leveraging BigInt support in JavaScript, this calculator can solve exact integers for any input, but limits the UI threshold to 170! to prevent browser rendering bottlenecks.
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